score:3

Accepted answer

i suspect you want:

var query = from entry in dbcontext.table1
            where entry.department == "abc" && entry.skillname != null
            select entry.skillname;

var count = query.distinct().count();

or using extension method syntax, in one go:

var count = dbcontext.table1
                     .where(entry => entry.department == "abc" && 
                                     entry.skillname != null)
                     .select(entry => entry.skillname)
                     .distinct()
                     .count();

as shown by mesiesta, you can combine query expressions with calls not supported within query expressions, but i tend to assign the query expression to an intermediate variable... i personally find it clearer, but use whichever you (and your team) prefer.

score:2

you can use linqpad to convert to linq and lambda expressions

score:3

something like this

 int count = (from p in table1
              where p.department == "abc" && p.skill_name != null
              select p.skill_name).distinct().count();

for second query you can use this

 var query= (from p in customer
             where p.customer_code=="1001"
             select new { location=p.location ,country=p.country}).distinct();

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